Photonic crystals are structures that possess spatial periodicities in refractive index, which lead to allowed and forbidden directions for light of certain energy and polarization to propagate. They have been the subject of considerable research and development efforts around the world due to their potential for controlling light in ways that cannot be achieved using homogeneous structures. Examples of extraordinary optical phenomena enabled by photonic crystals include reversed Doppler shifts, divergent-less super-lenses, negative refraction, and huge Verdet constants, to name just a few.
Recent theoretical investigations have predicted the existence of axially frozen modes that arise when light is incident upon an anisotropic two-dimensional photonic crystal. In theory, frozen modes can occur when the electromagnetic dispersion relationship, ω(k), exhibits a stationary inflection point. In this case, the group velocity approaches zero with negligible (possibly zero) reflections from the structure's surface and the mode amplitude within the photonic crystal structure can exceed that of the incident wave by several orders of magnitude. Such electromagnetic modes are of interest since they suggest a near-zero group velocity with extraordinary amplitudes.
Figotin, et al. (U.S. Pat. No. 6,701,048, which is incorporated herein by reference) discloses unidirectional gyrotropic photonic media that can allow axially frozen modes. The media include a sequence of parallel layers of two types of dielectric materials arranged in an alternating pattern, one material with an isotropic permittivity and the other with a permittivity tensor referred to the laboratory system with at least one non-zero off-diagonal element (i.e., ε12 and/or ε23≠0). Unfortunately, few naturally occurring dielectric materials meet the criteria including having off-diagonal ε elements so as to satisfy the permittivity requirement of the media disclosed in Figotin, et al. For example, possible naturally occurring materials could include certain crystals in triclinic or monoclinic classes. The patent discloses that some generic ferrite materials are available for use with microwave, millimeter wave, or submillimeter wave ranges, but discloses no possible materials for other frequency ranges.
In fact, it has been taught that at infrared and optical frequency ranges, finding appropriate materials for use in forming such media is highly problematic, and at frequencies above 1012 Hz, frozen mode formation has been considered to be impractical (see, for example, ‘Oblique frozen modes in periodic layered media’, A. Figotin and I. Vitebskiy, Physical Review E, 68, 036609 (2003)).
What is needed in the art are methods and materials for forming anisotropic one-dimensional photonic crystals capable of giving rise to axially frozen modes.